Why Prefix Search Using Trie in DSA Typescript?

The Big Idea

Discover how a simple tree can make searching words lightning fast!

The Scenario

Imagine you have a huge phone book and you want to find all contacts starting with "Sam". You flip pages one by one, checking each name carefully.

The Problem

This manual search is slow and tiring. You waste time checking every name, even those that don't start with "Sam". It's easy to miss some or get tired and make mistakes.

The Solution

A Trie is like a smart tree that organizes words by their letters. It lets you jump straight to all names starting with "Sam" without checking every entry. This saves time and effort.

Before vs After

✗ Before

function searchPrefix(words: string[], prefix: string): string[] {
  const result: string[] = [];
  for (const word of words) {
    if (word.startsWith(prefix)) result.push(word);
  }
  return result;
}

✓ After

class TrieNode {
  children: Map<string, TrieNode> = new Map();
  isEndOfWord: boolean = false;
}

class Trie {
  root = new TrieNode();
  // insert and prefix search methods here
}

What It Enables

It enables lightning-fast searches for all words sharing the same beginning letters, even in huge collections.

Real Life Example

When you type in a search bar on your phone, the suggestions appear instantly because the system uses a Trie to find words starting with what you typed.

Key Takeaways

Manual search checks every word, which is slow.

Trie organizes words by letters for quick prefix lookup.

Prefix search with Trie is fast and efficient for autocomplete.

Practice

1. What is the main purpose of using a Trie data structure in prefix search?

easy

A. To efficiently find all words that start with a given prefix

B. To sort words alphabetically

C. To store words in reverse order

D. To count the total number of words

Solution

1. Step 1: Understand Trie usage

   A Trie stores words by their prefixes, allowing quick prefix-based lookups.

2. Step 2: Identify prefix search goal

   Prefix search means finding all words starting with a given prefix efficiently.

3. Final Answer:

   To efficiently find all words that start with a given prefix -> Option A

4. Quick Check:

   Trie = Prefix search [OK]

Hint: Trie is built for prefix-based fast word retrieval [OK]

Common Mistakes:

• Confusing Trie with sorting structure
• Thinking Trie stores words reversed
• Assuming Trie counts total words only

2. Which of the following is the correct TypeScript syntax to define a Trie node with children as a Map and an endOfWord boolean?

easy

A. class TrieNode { children: object; endOfWord: string; constructor() { this.children = {}; this.endOfWord = ''; } }

B. class TrieNode { children: string[]; endOfWord: boolean; constructor() { this.children = []; this.endOfWord = false; } }

C. class TrieNode { children: Map; endOfWord: boolean; constructor() { this.children = new Map(); this.endOfWord = false; } }

D. class TrieNode { children: Map; endOfWord: boolean; constructor() { this.children = new Map(); this.endOfWord = false; } }

Solution

1. Step 1: Check children type

   Children should be a Map with string keys and TrieNode values for prefix characters.

2. Step 2: Check endOfWord type

   endOfWord is a boolean indicating if node ends a word.

3. Final Answer:

   class TrieNode { children: Map; endOfWord: boolean; constructor() { this.children = new Map(); this.endOfWord = false; } } -> Option D

4. Quick Check:

   Map + boolean endOfWord = class TrieNode { children: Map; endOfWord: boolean; constructor() { this.children = new Map(); this.endOfWord = false; } } [OK]

Hint: Use Map for children and boolean for endOfWord [OK]

Common Mistakes:

• Using array instead of Map for children
• Using wrong key type in Map
• Setting endOfWord as string instead of boolean

3. Given the following TypeScript code snippet, what will be the output of console.log(trie.startsWith('app'))?

class TrieNode {
  children = new Map();
  endOfWord = false;
}

class Trie {
  root = new TrieNode();

  insert(word: string) {
    let node = this.root;
    for (const char of word) {
      if (!node.children.has(char)) {
        node.children.set(char, new TrieNode());
      }
      node = node.children.get(char)!;
    }
    node.endOfWord = true;
  }

  startsWith(prefix: string): boolean {
    let node = this.root;
    for (const char of prefix) {
      if (!node.children.has(char)) return false;
      node = node.children.get(char)!;
    }
    return true;
  }
}

const trie = new Trie();
trie.insert('apple');
trie.insert('app');
trie.insert('bat');

medium

A. true

B. false

C. undefined

D. Error at runtime

Solution

1. Step 1: Insert words into Trie

   Words 'apple', 'app', and 'bat' are inserted, so prefix 'app' exists in Trie.

2. Step 2: Check startsWith method

   Method returns true if prefix characters exist in Trie nodes, which they do for 'app'.

3. Final Answer:

   true -> Option A

4. Quick Check:

   Prefix 'app' found = true [OK]

Hint: If prefix inserted, startsWith returns true [OK]

Common Mistakes:

• Confusing startsWith with search for whole word
• Expecting false if prefix is a word itself
• Thinking startsWith returns endOfWord status

4. The following TypeScript code tries to implement a startsWith method for a Trie but always returns false. What is the bug?

startsWith(prefix: string): boolean {
  let node = this.root;
  for (const char of prefix) {
    if (!node.children.has(char)) return false;
    node = node.children.get(char);
  }
  return false;
}

medium

A. It should check endOfWord before returning

B. It should use a for loop with index instead of for-of

C. It should return true after the loop if prefix exists

D. It should initialize node with a new TrieNode

Solution

1. Step 1: Analyze loop behavior

   The loop correctly traverses nodes for each prefix character.

2. Step 2: Check return statement

   Method returns false always after loop, so never returns true even if prefix found.

3. Step 3: Fix return logic

   Return true after loop if all prefix chars found.

4. Final Answer:

   It should return true after the loop if prefix exists -> Option C

5. Quick Check:

   Return true after loop if prefix found [OK]

Hint: Return true after loop if prefix nodes exist [OK]

Common Mistakes:

• Returning false at end regardless
• Checking endOfWord unnecessarily
• Incorrect node initialization

5. You want to extend a Trie to return all words starting with a given prefix. Which approach correctly implements this in TypeScript? A) Traverse to prefix node, then recursively collect all words below. B) Store all words in an array and filter by prefix each time. C) Use a hash map to map prefixes to words directly. D) Insert reversed words and search suffixes instead.

hard

A. Store all words in an array and filter by prefix each time.

B. Traverse to prefix node, then recursively collect all words below.

C. Use a hash map to map prefixes to words directly.

D. Insert reversed words and search suffixes instead.

Solution

1. Step 1: Understand prefix search extension

   To get all words with prefix, first find node matching prefix.

2. Step 2: Collect words recursively

   From prefix node, recursively traverse children to collect all complete words.

3. Step 3: Evaluate other options

   Filtering array or hash map is less efficient; reversed words search suffixes, not prefixes.

4. Final Answer:

   Traverse to prefix node, then recursively collect all words below. -> Option B

5. Quick Check:

   Recursive traversal from prefix node = Traverse to prefix node, then recursively collect all words below. [OK]

Hint: Find prefix node, then DFS to collect words [OK]

Common Mistakes:

• Filtering all words each time (slow)
• Using hash map without prefix traversal
• Confusing prefix with suffix search